Nonlocal Mathematical Morphology and Spatially-Variant Connected operators

This paper proposes a new method to generate adaptive structuring elements (SEs) for building spatially-variant morphological operators. First, novel nonlocal SE is introduced as a new special case of spatially-variant morphological flat kernel. In the design of nonlocal SE, nonlocal patch distance is used to construct the neighborhood of SE. Indeed, the neighborhood of SE is divided into two parts: one is the kernel center, and another is the kernel boundary, by which the nonlocal patch distance and bilateral distance are both taken into consideration. Second, a new type of nonclassical connectivity is defined, where the connectivity rely on nonlocal patch-wise path connectedness relation. This definition means that the new connected operators are spatially-variant and can produce transforms having the properties of an algebraic opening (resp. closing). Then, we illustrate the nonlocal morphological operators for medical image restoration and target detection. Experimental results on real images show that our methods produce excellent results.